# Greek Mathematics

# I. Introductory

## (a) Mathematics and its Divisions

### (i.) Origin of the Name

### Anatolius ap. Her. Def., ed. Heiberg 160. 8–162. 2

### Ἐκ τῶν Ἀνατολίου . . .

“Ἀπὸ τίνος δὲ μαθηματικὴ ὠνομάσθη;

“Οἱ μὲν ἀπὸ τοῦ Περιπάτου φάσκοντες ῥητορικῆς μὲν καὶ ποιητικῆς συμπάσης τε τῆς δημώδους μουσικῆς δύνασθαί τινα συνεῖναι καὶ μὴ μαθόντα, τὰ δὲ καλούμενα ἰδίως μαθήματα οὐδένα εἰς εἴδησιν λαμβάνειν μὴ οὐχὶ πρότερον ἐν μαθήσει γενόμενον τούτων, διὰ τοῦτο μαθηματικὴν καλεῖσθαι τὴν περὶ τούτων θεωρίαν ὑπελάμβανον. θέσθαι δὲ λέγονται τὸ τῆς μαθηματικῆς ὄνομα ἰδιαίτερον ἐπὶ μόνης γεωμετρίας καὶ ἀριθμητικῆς οἱ ἀπὸ τοῦ Πυθαγόρου· τὸ γὰρ πάλαι χωρὶς ἑκατέρα τούτων ὠνομάζετο, κοινὸν δὲ οὐδὲν ἦν ἀμφοῖν ὄνομα.”

# Introductory

# I. Introductory

## (a) Mathematics and its Divisions

### (i.) Origin of the Name

### Anatolius, cited by Heron, Definitions, ed. Heiberg 160. 8–162. 2

### From the works of Anatolius^{a} . . .

“Why is mathematics so named?

“The Peripatetics say that rhetoric and poetry and the whole of popular music^{b} can be understood without any course of instruction, but no one can acquire knowledge of the subjects called by the special name mathematics unless he has first gone through a course of instruction in them; and for this reason the study of these subjects was called mathematics.^{c} The Pythagoreans are said to have given the special name mathematics only to geometry and arithmetic; previously each had been called by its separate name, and there was no name common to both.”^{d}

^{a}Anatolius was bishop of Laodicea about a.d. 280. In a letter by Michael Psellus he is said to have written a concise treatise on the Egyptian method of reckoning.^{b}i.e. singing or playing, as opposed to the mathematical study of musical intervals.^{c}The word μάθημα, from μαθεῖν, means in the first place “that which is learnt.” In Plato it is used in the general sense for any subject of study or instruction, but with a tendency to restrict it to the studies now called mathematics. By the time of Aristotle this restriction had become established.^{d}The esoteric members of the Pythagorean school, who had learnt the Pythagorean theory of knowledge in its entirety, are said to have been called mathematicians (μαθηματικοί), whereas the exoteric members, who merely knew the Pythagorean rules of conduct, were called hearers (ἀκουσματικοί). See Iamblichus, De Vita Pythag. 18. 81, ed. Deubner 46. 24 ff.